SOLUTION: The ratio of a boy’s age to his father’s age is 1 : 4. In 4 years’ time, the ratio of their ages will be 1 : 3. How old is the boy now?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of a boy’s age to his father’s age is 1 : 4. In 4 years’ time, the ratio of their ages will be 1 : 3. How old is the boy now?      Log On


   



Question 614316: The ratio of a boy’s age to his father’s age is 1 : 4. In 4 years’ time, the ratio of their ages will
be 1 : 3. How old is the boy now?

Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
boy's age be x
and father's age =y
x%2Fy+=+1%2F4
so y= 4x
In 4 years their ages will be
x+4 & y+4
%28x%2B4%29%2F%28y%2B4%29+=+1%2F3
cross multiply
3(x+4) = (y+4)
substitute y
3x+12=4x+4
4x-3x=12-4
x=8 the boy's age

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = boy's age now
Let +b+ = Father's age now
given:
(1) +a%2Fb+=+1%2F4+
(2) +%28+a+%2B+4+%29+%2F+%28+b+%2B+4+%29+=+1%2F3+
--------------------------
(1) +4a+=+b+
By substitution:
(2) +%28+a+%2B+4+%29+%2F+%28+4a+%2B+4+%29+=+1%2F3+
(2) +3%2A%28+a+%2B+4+%29+=+4%2A%28+a+%2B+1+%29+
(2) +3a+%2B+12+=+4a+%2B+4+
(2) +a+=+8+
and
(1) +a%2Fb+=+1%2F4+
(1) +8%2Fb+=+1%2F4+
(1) +32+=+b+
The boy is 8 now
check:
(2) +%28+a+%2B+4+%29+%2F+%28+b+%2B+4+%29+=+1%2F3+
(2) +%28+8+%2B+4+%29+%2F+%28+32+%2B+4+%29+=+1%2F3+
(2) +12+%2F+36+=+1%2F3+
(2) +3%2A12+=+36+
(2) +36+=+36+
OK